QUASIHYPERBOLIC METRIC AND QUASISYMMETRIC MAPPINGS IN METRIC SPACES

被引：27
作者：
Huang, Xiaojun [1 ,2 ]
Liu, Jinsong [3 ,4 ]
机构：
[1] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China
[2] Math Sci Res Inst Chongqing, Chongqing 401331, Peoples R China
[3] Chinese Acad Sci, HUA Loo Keng Key Lab Math, Beijing 100190, Peoples R China
[4] Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2015年 / 367卷 / 09期
关键词：
FREE QUASICONFORMALITY; MAPS;
D O I：
10.1090/S0002-9947-2015-06240-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we prove that the quasihyperbolic metrics are quasi-invariant under a quasisymmetric mapping between two suitable metric spaces. Meanwhile, we also show that quasi-invariance of the quasihyperbolic metrics implies that the corresponding map is quasiconformal. At the end of this paper, as an application of these theorems, we prove that the composition of two quasisymmetric mappings in metric spaces is a quasiconformal mapping.
引用
收藏
页码：6225 / 6246
页数：22
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